Problem: Simplify the following expression: $p = \dfrac{5k^2 + 25k - 30}{k - 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ p =\dfrac{5(k^2 + 5k - 6)}{k - 1} $ Then we factor the remaining polynomial: $k^2 + {5}k {-6} $ ${-1} + {6} = {5}$ ${-1} \times {6} = {-6}$ $ (k {-1}) (k + {6}) $ This gives us a factored expression: $\dfrac{5(k {-1}) (k + {6})}{k - 1}$ We can divide the numerator and denominator by $(k + 1)$ on condition that $k \neq 1$ Therefore $p = 5(k + 6); k \neq 1$